Solve Using the Quadratic Formula 9x^2+30x+25=0

$9 x^{2} + 30 x + 25 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 9$ , $b = 30$ , and $c = 25$ into the quadratic formula and solve for $x$ .

$\frac{- 30 \pm \sqrt{30^{2} - 4 \cdot (9 \cdot 25)}}{2 \cdot 9}$

Step 3

Simplify.

Simplify the numerator.

Raise $30$ to the power of $2$ .

$x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 9 \cdot 25}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot 25$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 30 \pm \sqrt{900 - 36 \cdot 25}}{2 \cdot 9}$

Multiply $- 36$ by $25$ .

$x = \frac{- 30 \pm \sqrt{900 - 900}}{2 \cdot 9}$

Subtract $900$ from $900$ .

$x = \frac{- 30 \pm \sqrt{0}}{2 \cdot 9}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 30 \pm \sqrt{0^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 30 \pm 0}{2 \cdot 9}$

$- 30$ plus or minus $0$ is $- 30$ .

$x = \frac{- 30}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 30}{18}$

Cancel the common factor of $- 30$ and $18$ .

Factor $6$ out of $- 30$ .

$x = \frac{6 (- 5)}{18}$

Cancel the common factors.

Factor $6$ out of $18$ .

$x = \frac{6 \cdot - 5}{6 \cdot 3}$

Cancel the common factor.

$x = \frac{6 \cdot - 5}{6 \cdot 3}$

Rewrite the expression.

$x = \frac{- 5}{3}$

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{5}{3}$ Double roots